DAG: A Dual Causal Network for Time Series Forecasting with Exogenous Variables

2025-09-18

AI Summary

Existing exogenous-variable-enhanced time series forecasting (TSF-X) methods suffer from two key limitations: (1) they neglect future exogenous inputs, and (2) they fail to model the dynamic causal relationships between endogenous and exogenous variables. To address these issues, we propose DAG, a dual-causal graph framework that unifies causal discovery and injection along both temporal and channel dimensions. Along the temporal dimension, DAG identifies causal effects of historical exogenous variables on future target values; along the channel dimension, it explicitly models cross-variable influence pathways from exogenous to endogenous variables. Crucially, DAG fully incorporates observable future exogenous inputs and yields interpretable causal structures. Extensive experiments on multiple real-world datasets demonstrate that DAG significantly outperforms state-of-the-art TSF-X baselines—particularly under settings where future exogenous variables are available—achieving substantial improvements in forecasting accuracy.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Time series forecasting is crucial in various fields such as economics, traffic, and AIOps. However, in real-world applications, focusing solely on the endogenous variables (i.e., target variables), is often insufficient to ensure accurate predictions. Considering exogenous variables (i.e., covariates) provides additional predictive information, thereby improving forecasting accuracy. However, existing methods for time series forecasting with exogenous variables (TSF-X) have the following shortcomings: 1) they do not leverage future exogenous variables, 2) they fail to account for the causal relationships between endogenous and exogenous variables. As a result, their performance is suboptimal. In this study, to better leverage exogenous variables, especially future exogenous variable, we propose a general framework DAG, which utilizes dual causal network along both the temporal and channel dimensions for time series forecasting with exogenous variables. Specifically, we first introduce the Temporal Causal Module, which includes a causal discovery module to capture how historical exogenous variables affect future exogenous variables. Following this, we construct a causal injection module that incorporates the discovered causal relationships into the process of forecasting future endogenous variables based on historical endogenous variables. Next, we propose the Channel Causal Module, which follows a similar design principle. It features a causal discovery module models how historical exogenous variables influence historical endogenous variables, and a causal injection module incorporates the discovered relationships to enhance the prediction of future endogenous variables based on future exogenous variables.

Problem

• Leveraging future exogenous variables in time series forecasting
• Modeling causal relationships between endogenous and exogenous variables
• Improving forecasting accuracy through dual causal networks

Innovation

• Dual causal network for temporal and channel dimensions
• Causal discovery modules for exogenous variable relationships
• Causal injection modules to enhance forecasting accuracy